Answer
Initial amount $a=12$
Rate of growth $r=5\%$
At $t=5,y=15.3$
Work Step by Step
The given expression is
$\Rightarrow y=12(1.05)^t$
$\Rightarrow y=12(1+0.05)^t$
The standard form of the exponential growth function is
$y=a(1+r)^t$
Initial amount $a=12$
Rate of growth $r=0.05=5\%$
Substitute $5$ for $t$.
$\Rightarrow y=12(1+0.05)^5$
Simplify.
$\Rightarrow y=12(1.05)^5$
Evaluate the power.
$\Rightarrow y=12(1.2762815625)$
Simplify.
$\Rightarrow y=15.31537875$
Round to the nearest tenth.
$\Rightarrow y=15.3$.
